Differential Topology: Notational Illusion Leading Away From Nordstr?m's Aether into General Relativity
|Title||Differential Topology: Notational Illusion Leading Away From Nordstr?m\'s Aether into General Relativity|
By 1914, a scalar Lorentz covariant gravitational theory advanced by Finnish physicist Gunnar Nordstr?m had been developed, with the assistance of Einstein and Fokker, to the point it seemed to profoundly challenge the developing General Theory of Relativity. One major difference though was that it did not seem to predict the gravitational deflection of light. After this phenomenon was empirically observed, the theory was relegated mainly to the history books as General Relativity took off. We present in this paper an argument based upon our fundamental understandings of Lagrangian mechanics, the Action Principle and Calculus that the scalar argument used by Nordstr?m and Einstein is fundamentally and indefensibly restrictive. Using plots of linearized gravity we demonstrate that the cosmological constant problem, touted as the worst theoretical prediction in physics, can most plausibly be solved by a change of our understanding of the magnitude relationships between vacuum and baryonic energy density. These plots will also demonstrate our argument that derivatives of functions are a notational shortcut for tangents of integrals, and that "tangents of lines" (differential topology) are a basic misunderstanding of the Fundamental Theorem of Calculus. The D'alembertian equation of this, using the same arguments of hydrodynamics which led to Max von Laue's stress-energy tensor, seems to naturally lead to a Lorentz covariant aether theory that should be able to account for General Relativity, Quantum Field Theory and plausibly "dark energy". We also consider whether this aether theory can present a second gradient via a spatial change in vacuum energy density which is similar in effect to MOND in order to account for "dark matter" effects.